The intermittency and variability inherent to many waste heat sources have largely been overlooked in existing studies of membrane distillation (MD). In the current study, MD system operation with intermittent and variable temperature waste heat was assessed with two system arrangements: "direct" and "indirect." In the direct arrangement, the heat exchanger and membrane module are in a single loop; in the indirect arrangement, they are in two separate loops. Modeling results indicate the direct arrangement produced 17.7% more water at 12.5% intermittency and the indirect arrangement produced 21.5% more water at 87.5% intermittency, due to the indirect arrangement's ability to store more heat when the waste heat source is on. Waste heat variability was strongly reflected in water flux profiles, but the indirect arrangement showed significantly less water flux variability more than two times less in modeling analyses with intermittent waste heat and 30.4% less in variable-temperature experiments. Lower water flux variability in the indirect arrangement translates to better system controllability, even when the direct arrangement produces more water. The advantages of each arrangement identified in the current study give system designers key information to improve water production, heat storage, and/or system control in different waste heat scenarios.